Games simply don't benefit enough for the cost of a new processor, let alone new motherboard and ram.
A new GPU will almost always the best bang for your buck improvement in games.
Then you should definitely go AMD. There is literally no reason not to unless you are already using cuda or ray tracing a ton. AMD is the best value for the money by far, has a MUCH better software interface (never thought I would say that), comparable or less driver issues than nvidia now, and it also works flawlessly on Linux, including full undervolting support (important on any GPU, but on AMD it is much easier).
That being said, if comparable performance GPUs are the same price in your region and you use windows, nvidia is also fine to grab.
Always undervolt your GPU. My 5700XT that ran on 200W before now maxes out at 150W and usually is at 140W with a 1% performance difference. That is like a 9C temp difference.